"[Summers'] removal means Janet Yellen is a near certainty. Her dovish-ness will be highly supportive to emerging market currencies and you can already see that in early trade," said Evan Lucas, market strategist at IG. The rupee strengthened on the news in early Asian trade on Monday opening over 1 percent higher from Friday's levels.

According to Steven Englander, global head of G10 FX Strategy at CitiFX, currencies from countries with larger current account deficits are in line for a boost now Summers has been removed from the running.

"The main buying opportunities are probably high current account deficit emerging markets, Aussie dollar and the yen," he said.

"In that vein, Lawrence Summers' withdrawal from next Fed Chair(person) race leaves the field open for Fed Vice-Chair Yellen and USD on the back foot," said Vishnu Varathan, market economist, at Mizuho bank.

"Overall, it looks like a 'risk on' bet with the AUD's knee-jerk jump as proof of the pudding," he added, referring to strength in the Aussie dollar, which rallied roughly 0.8 percent by mid-morning in Australia on Monday.

Meanwhile, Richard Yetsenga, head of global markets research at Australia's ANZ bank, said there was "no question" that Summers' withdrawal would help emerging market currencies in the short term, singling out the Indian rupee as a key beneficiary.

"India... is a better case than Indonesia because at least it has allowed its currency to adjust and policy has responded reasonably forcefully.

Indonesia has been relying a lot more on currency intervention to keep the currency stable and hasn't allowed the degree of adjustment we've seen in India," he added.

Emerging markets have seen a broad selloff since the Fed tapering talk first gripped markets over three months ago. The Indonesian rupiah has lost 16.5 percent since late May, while the Indian rupee plummeted to a record low of 68.8 against the dollar on August 28, though it has stabilized somewhat over the past week.

The U.S. dollar index weakened by roughly 0.4 percent on the news of Summers' exit over the weekend to trade at around 81.131 in Asia on Monday morning.